Quantum multiparameter estimation with multi-mode photon catalysis entangled squeezed state

TL;DR

This paper introduces a method to generate multi-mode entangled squeezed vacuum states via photon catalysis, enhancing multi-parameter quantum estimation precision and robustness against photon loss in quantum metrology.

Contribution

The authors propose a novel approach to produce multi-mode entangled states using cross-Kerr nonlinearities and Fredkin gates, improving phase estimation bounds and robustness.

Findings

QCRB improves with more catalytic photons or lower beam splitter transmissivity.

Photon catalysis states outperform ideal entangled states under photon loss.

Method enhances multi-parameter quantum metrology applications.

Abstract

We propose a method to generate the multi-mode entangled catalysis squeezed vacuum states (MECSVS) by embedding the cross-Kerr nonlinear medium into the Mach-Zehnder interferometer. This method realizes the exchange of quantum states between different modes based on Fredkin gate. In addition, we study the MECSVS as the probe state of multi-arm optical interferometer to realize multi-phase simultaneous estimation. The results show that the quantum Cramer-Rao bound (QCRB) of phase estimation can be improved by increasing the number of catalytic photons or decreasing the transmissivity of the optical beam splitter using for photon catalysis. In addition, we also show that even if there is photon loss, the QCRB of our photon catalysis scheme is lower than that of the ideal entangled squeezed vacuum states (ESVS), which shows that by performing the photon catalytic operation is more robust against photon loss than that without the catalytic operation. The results here can find important applications in quantum metrology for multiparatmeter estimation.